Can entangled electrons in helium be observed and measured in practice?

[Andrew Wright]

TL;DR Summary

If two electrons in a helium atom are entangled, will measuring the location of one reveal anything about the other?

If you measure the location of an electron in helium, does it impact the expectation value for the location of the other? Also, can this experiment be conducted in practice? Thanks.

 

[hilbert2]

I'm not sure how to do this kind of an experiment, but any measurement that reveals the position of an electron with high accuracy will make it unlikely to find any other electron very close to it right after the first measurement. It's just about the Coulomb repulsive force, and possibly also the antisymmetry requirement of a system of identical fermions.

 

[Vanadium 50]

There really isn't "one electron" and "the other electron". There is one and only one electron wavefunction, and electrons are indistinguishable.

Additionally, you need to be very, very careful about what measurement actually is. For example, you could discuss <r_1 - r_2>.

 

[Andrew Wright]

I read somewhere that high frequency radiation can locate electrons.

 

[PeroK]

I read somewhere that high frequency radiation can locate electrons.

I imagine this relates more to helium ionization. A question might be: what is the expected state of the helium ion after ionization by a high energy photon?

PS There's a related question here:

https://physics.stackexchange.com/q...ually-observe-the-position-of-the-electron-in

 

[Vanadium 50]

. A question might be: what is the expected state of the helium ion after ionization by a high energy photon?

Isn't that just a one-electron atom?

 

[Vanadium 50]

I read somewhere

You're going to have to be more specific than that if you want us to comment intelligently on what you read.

 

[PeroK]

Isn't that just a one-electron atom?

Yes, but it puts the conceptual nature of the question in some context. I.e. what happens when a photon interacts with an atom.

 

[Andrew Wright]

You're going to have to be more specific than that if you want us to comment intelligently on what you read.

So in this link, there is a quotation of Hakwin's Brief history of time (where I also read it) that discusses short wavelength/high frequency measurement of an electron's position. I know that this is not-at-all in the context of a helium atom, but it does appear to be a general principle of physics rather than a feature of just one experiment.

https://physics.stackexchange.com/q...measure-the-position-of-a-particle-accurately

Hope this explains a little where I am coming from. I am imagining locating an electron within a helium atom (perhaps using radiation).

 

[Andrew Wright]

OK, so I have been trying to educate myself on this matter. I watched this video to calculate the probability of finding an electron outside the Bhor radius in Hydrogen.

https://www.bing.com/videos/search?...1494AC5F5E1CB1641047149&view=detail&FORM=VIRE

However, I feel unsure how electrons can be found with any accuracy at these distances. What I mean is that an electron microscope could probe nature at distances of 0.2nm. This is only about the radius of a helium atom. So what sort of experiment can find the location of anything within atomic distances?

 

[Andrew Wright]

PS There's a related question here:

https://physics.stackexchange.com/q...ually-observe-the-position-of-the-electron-in

Thanks for the link. "Photoionization microscopy" looks pretty cool. Looking at that research in more detail, helium and entangled electrons are mentioned and were being studied. That was a few years ago now:)